Skip to main content

Part of the book series: Texts in Applied Mathematics ((TAM,volume 50))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 84.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

14.7 Guide to the Literature

  1. Ablowitz, M.J. and Benney, D.J. (1970), The evolution of multi-phase modes for nonlinear dispersive waves, Stud. Appl. Math. 49, pp. 225–238.

    MATH  Google Scholar 

  2. Benney, D.J. and Newell, A.C. (1967), The propagation of nonlinear wave envelopes, J. Math. Phys. 46, pp. 133–139.

    MATH  MathSciNet  Google Scholar 

  3. Bourland, F.J. and Haberman, R. (1989), The slowly varying phase shift for perturbed, single and multi-phased strongly nonlinear dispersive waves, Physica 35D, pp. 127–147.

    MathSciNet  Google Scholar 

  4. Chikwendu, S.C. and Kevorkian, J. (1972), A perturbation method for hyperbolic equations with small nonlinearities, SIAM J. Appl. Math. 22, pp. 235–258.

    Article  MATH  MathSciNet  Google Scholar 

  5. Chikwendu, S.C. and Easwaran, C.V. (1992), Multiple scale solution of initial-boundary value problems for weakly nonlinear wave equations on the semiinfinite line, SIAM J. Appl. Math. 52, pp. 946–958.

    Article  MATH  MathSciNet  Google Scholar 

  6. de Jager, E.M. and Jiang Furu (1996), The Theory of Singular Perturbations, Elsevier, North-Holland Series in Applied Mathematics and Mechanics 42, Amsterdam.

    Google Scholar 

  7. Haberman, R. and Bourland, F.J. (1988), Variation of wave action: modulations of the phase shift for strongly nonlinear dispersive waves with weak dissipation, Physica D 32, pp. 72–82.

    Article  MATH  MathSciNet  Google Scholar 

  8. Kevorkian, J.K. and Cole, J.D. (1996), Multiple Scale and Singular Perturbation Methods, Springer-Verlag, New York.

    MATH  Google Scholar 

  9. Luke, J.C. (1966), A perturbation method for nonlinear dispersive wave problems, Proc. R. Soc. London Ser. A, 292.

    Google Scholar 

  10. McLaughlin, D.W. and Scott, A.C. (1978), Perturbation analysis of fluxon dynamics, Phys. Rev. A 18, pp. 1652–1680.

    Article  Google Scholar 

  11. Scott, A. (1999), Nonlinear Science: Emergence and Dynamics of Coherent Structures, Oxford University Press, Oxford.

    MATH  Google Scholar 

  12. Van der Burgh, A.H.P. (1979), On the asymptotic validity of perturbation methods for hyperbolic differential equations, in Asymptotic Analysis, from Theory to Application (Verhulst, F., ed.) Lecture Notes in Mathematics 711, pp. 229–240, Springer-Verlag, Berlin.

    Google Scholar 

  13. Whitham, G.B. (1970), Two-timing, variational principles and waves, J. Fluid. Mech. 44, pp. 373–395.

    Article  MATH  MathSciNet  Google Scholar 

  14. Whitham, G.B. (1974), Linear and Nonlinear Waves, John Wiley, New York.

    MATH  Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science+Business Media, Inc.

About this chapter

Cite this chapter

(2005). Wave Equations on Unbounded Domains. In: Methods and Applications of Singular Perturbations. Texts in Applied Mathematics, vol 50. Springer, New York, NY. https://doi.org/10.1007/0-387-28313-7_14

Download citation

Publish with us

Policies and ethics